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An investigation into the effect of carbon on the kinetics of dynamic restoration and flow behavior of carbon steels
Mechanics of Materials 35 (2003) 653–660 www.elsevier.com/locate/mechmat
An investigation into the effect of carbon on the kinetics of dynamic restoration and flow behavior of carbon steels Siamak Serajzadeh *, Ali Karimi Taheri Department of Materials Science and Engineering, Sharif University of Technology, Azadi Ave., PO Box 11365-9466, Tehran, Iran Received 15 March 2002; received in revised form 21 August 2002
Abstract A study has been made to determine the influence of the carbon content on the kinetics of dynamic recrystallization and recovery as well as flow stress during hot deformation of carbon steels. For this purpose, single hit hot compression experiments at various strain rates and temperatures on two grades of carbon steel together with the Avrami-type kinetics equation and Bergstrom approach have been utilized. The results show that the apparent hot deformation activation energy decreases with increasing carbon content and this phenomenon results in a faster dynamic recrystallization and recovery and a lower flow stress at high temperatures and/or low strain rates in high carbon steels, while at low temperatures and/or high strain rates the low carbon steel has a lower flow stress and higher rate of dynamic recovery. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Phase transformation; Hot compression test; Carbon steel; Flow stress
1. Introduction The flow behavior of steel has always been of importance, because of its strong influence on the microstructure and mechanical properties of the final product. Different factors may alter the flow behavior during the hot deformation of metals. Among these factors the chemical composition has a strong role (Dieter, 1987). Carbon is one of the most important alloy elements which can change the flow behavior as well as the microstructure and kinetics of metallurgical transformation of steel.
*
Corresponding author. Tel.: +98-602-2721; fax: +98-6005717. E-mail address: [email protected] (S. Serajzadeh).
However, there are limited studies dealing with the effect of carbon content on the hot deformation of steels. Wray (1982, 1984) performed hot tension tests at different temperatures to determine the effect of carbon on the flow stress at low strain rates of 6 106 to 2 102 s1 . He reported that increasing the carbon content decreased the work hardening and flow stress of steel. He also suggested an exponentional relationship between the flow stress and temperature. Jaipal et al. (1997) investigated the flow stress and dynamic recrystallization in low and high carbon steel employing a wide range of strain rates. The results of their work show that increasing the carbon content decreased the flow stress of steel at low strain rates and/or high temperatures. Moreover, they reported that at very high strain rates or low temperatures,
0167-6636/03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0167-6636(02)00291-0
654
S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
the peak flow stress of high carbon steel would be higher than that of low carbon steel. Kong et al. (1998) have modeled the effect of carbon content on the hot strength of steel. They demonstrated that increasing the carbon content decreases the flow stress at low strain rates and/or high temperatures whilst at high strain rates and/or low temperatures the low carbon steel has a lower flow stress especially at the initial stage of deformation. The effect of carbon and initial austenite grain size on the austenite flow stress were studied by Dixon et al. (1996). They demonstrated that low carbon steels have a higher strength at strain rates below 1 s1 . Above 1 s1 high carbon steels are stronger and also, there is a little change in recrystallization kinetics between low and high carbon steels. Although the effect of carbon on hot deformation of steel has been studied, because of the complex role of carbon on the flow behavior of steel the study of the effect of carbon on restoration phenomenon in steel requires further investigation. In the present paper, hot compression tests at different strain rates and temperatures were used to study the effect of carbon content and initial austenite grain size on the kinetics of dynamic recrystallization and recovery as well as on the flow behavior of steel in the austenite range. Also, a mathematical model of the flow stress and the kinetics of dynamic recrystallization and recovery via the Bergstrom approach (1970) and the Avrami-type equation will be presented.
2. Transformation and flow stress model
q ¼ q0
ð1Þ
at e ¼ 0
ð2Þ
So, the dislocation density variations during hot deformation can be described as U Xe U Xe e þ q0 q¼e ð3Þ X X Utilizing Eq. (1) and calculating dislocation density for the steady state flow stress condition, we have dq ¼ 0; de
qRec ¼
U X
ð4Þ
Also, using the classic relationship between stress and dislocation density (Honeycombe, 1981), r ¼ aGbq0:5 , and employing Eqs. (3) and (4), it can be found that the variation of flow stress due to dynamic recovery during hot deformation is as follows: r2 ¼ r2Rec þ ðr20 r2Rec ÞeXe ð5Þ where r is the instantaneous flow stress, r0 and rRec are the initial flow stress and the steady state flow stress due to dynamic recovery, respectively. During hot deformation, one may ignore the initial flow stress due to its low magnitude (Colas, 1996). In this condition Eq. (5) can be written as XR ¼
Various models have been proposed to describe the flow stress of metals during hot deformation incorporating dynamic recrystallization and recovery (Bergstrom, 1970; Estrin and Mecking, 1984). Most of these approaches are based on the balance between work hardening and work softening due to dislocation multiplication and annihilation during hot deformation. Bergstrom (1970) has derived the variation of dislocation density according to work hardening and softening as follows: dq ¼ U Xq de
where U represents the work hardening and X describes the amount of the dynamic recovery during hot deformation. Assuming U and X are strain independent, the above differential equation can be easily solved using the following initial condition:
r2 ¼ 1 expðXeÞ ðe < ec Þ r2Rec
ð6Þ
here XR represents the fraction of dynamic recovery. At high temperatures and low strain rates dynamic recrystallization can occur. In this situation the effect of dynamic recrystallization can be assessed using the Avrami equation (Sellars and Whiteman, 1979) as presented below: n e ec d XD ¼ 1 exp k ð7Þ ðe P ec Þ ep where XD is dynamic recrystallization volume fraction, k and nd are dynamic recrystallization parameters depending on chemical composition
S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
and hot deformation conditions (Colas, 1996), ec is the critical strain for occurring dynamic recrystallization which has been taken 0:8ep (Sellars and Whiteman, 1979) and ep is the peak strain which can be expressed by the following relationship: ep ¼
Ad0q zm
ð8Þ
where z is the Zener–Hollomon parameter, z ¼ e_ expðQdef =RT Þ, and d0 is the initial austenite grain size. It is worth noting that for determining the progress of dynamic recrystallization, XD , the following expression was employed: rRec r XD ¼ ð9Þ rp rRex Here, rRex and rp are the steady state flow stress due to dynamic recrystallization and peak flow stress, respectively. rRec was derived through an extrapolation method using MATLAB. With the aid of Eqs. (6), (7) and (9), the flow stress of steel during hot deformation can be described. It is worth noting that parameters such as rRex , r0 , rRec , X and k are a function of deformation process (Dieter, 1987). They may be described using the Zener–Hollomon parameter while Qdef can be determined by the following relationship (Kong et al., 1998): Q oðln e_Þ ¼ 1 ð10Þ R o T rss
3. Materials and experimental procedures The materials used in this research consisted of two grades of carbon steel with the chemical compositions shown in Table 1. To remove the casting structure, the steels were heated up to 1250 °C and rolled at this temperature. Hot compression samples were machined out of the as received hot rolled bars with the deformation axis parallel to hot rolling direction. A height to diameter ratio of 1.5 was selected for the samples to ensure homogeneous deformation. The hot deformation experiments were conducted on a computerized servohydraulic MTS machine with maximum capacity of 100 kN. Experiments were carried out at
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Table 1 Chemical composition of the high and low carbon steels (wt.%) C
Mn
Si
P (max)
S (max)
Cr (max)
N (ppm)
B (ppm)
0.7 0.1
0.55 0.5
0.08 0.04
0.03 0.025
0.03 0.025
0.08 0.07
120 80
15 5
Table 2 The deformation parameters used for hot compression tests Temperature (°C)
Strain-rate (s1 )
900 950 1000 1050 1100 1150 1200
0.01 0.1 0.5 1 1.5 2 3
temperatures of 900–1200 °C with strain rates varying between 0.01 and 3 s1 . The employed deformation parameters for the single hit hot compression experiments are presented in Table 2. All samples were heated to 1200 °C and held for 10 min at this temperature and then cooled to the deformation temperature and held for 3 min to eliminate the thermal gradient before deformation at the appropriate true strain rate. To determine the effect of initial austenite grain size the above procedures were performed at different holding times of 20 and 30 min at different temperatures. To reveal the initial austenite grain size an etching solution based on saturated picric acid was utilized at 60 and 80 °C for the high and low carbon steel, respectively.
4. Results and discussion Examples of the stress–strain curves gained from the hot compression tests for the low and high carbon steel are presented in Figs. 1 and 2, respectively. As it is seen from the figures the shapes of all curves are similar to the classical stress–strain curves consisting of initial work hardening at lower strains followed by work softening and a peak in flow stress and then the steady
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S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
state flow stress region at higher strains. Also, it is observed that for both kinds of steels increasing the strain rate leads to a larger peak in strain and stress. It is worth noting that the high carbon steel has a lower overall flow stress in comparison with the low carbon steel. In addition the peak strain occurs at smaller strains in the high carbon steel. However, at higher strain rates the situation is changed and the low carbon steel has a lower overall flow stress. Based on the data obtained from the hot deformation tests and Eqs. (6) and (7) the following equations for describing the kinetics of dynamic recrystallization and recovery kinetics as well as instantaneous flow stress of steels were derived: low carbon steel: r2 ¼ r2Rec ð1 expð520d00:3 z0:08 eÞÞ ðe 6 ec Þ i h XD ¼ 1 exp 17:2 104 d00:48 z0:23 ðeec Þ1:6
ð11Þ
ðe P ec Þ Fig. 1. Stress–strain curves for the low carbon steel at 1000 °C.
ep ¼ 6:5 104 d00:43 z0:132
high carbon steel: r2 ¼ r2Rec ð1 expð230d00:22 z0:06 eÞÞ ðe 6 ec Þ i h XD ¼ 1 exp 85:5 104 d00:46 z0:3 ðe ec Þ1:8
ð12Þ
ðe P ec Þ ep ¼ 2:5 103 d00:4 z0:1
Fig. 2. Stress–strain curves for the high carbon steel at 1000 °C.
The comparison between the derived stress–strain curves by Eqs. (11) and (12) and experimental stress–strain ones for both the low and the high carbon steels are presented in Figs. 3 and 4, respectively. It can be observed that there is a good agreement between the two sets of data that confirms the validity of the model and the assumptions as well as the derived rate equations of the dynamic recovery and recrystallization. Employing Eq. (10), the activation energies for the low carbon and the high carbon steel were calculated, at steady state stresses less than 100 MPa, as 338 and 316 kJ/mole, respectively. In such a condition, it is expected that the higher activation energy causes a higher Zener–Hollomon factor at an equivalent temperature and strain rate, and therefore, for the high carbon steel the onset of dynamic recrystallization occurs at lower strains
S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
657
Fig. 3. Derived and experimental stress–strain curves for the low carbon steel.
Fig. 4. Derived and experimental stress–strain curves for the high carbon steel.
since the kinetics of dynamic recrystallization is fast as compared to that of the low carbon steel as shown in Fig. 5. This phenomenon decreases the hot strength of the high carbon steel. Furthermore, in addition to the activation energy, the exponent nd can also influence the rate of recrystallization. Regarding Eqs. (11) and (12) (XD ) it is observed that this parameter is 1.8 and 1.6 for the high and low carbon steels, respectively. This follows faster dynamic recrystallization kinetics as presented in Fig. 5. This may be attributed to the effect of carbon on lattice expansion and resulting increase in self-diffusion rate at the high carbon steel (Wray, 1982), which can increase the rate of dynamic recrystallization and recovery in diffusioncontrolled processes. It should be noted that for large Zener–Hollomon parameter (i.e. high strain rates and/or low temperatures) dynamic recrystallization is postponed and the dominant softening mechanism would be only dynamic recovery. Additionally, at high strain rates the recovery
process is controlled by cross slip process (Honeycombe, 1981). It is expected that under this condition, carbon increases the flow stress of steel due to its effect on reduction of stacking fault energy and increase in critical stress for cross slip. Therefore, carbon decreases the rate of dynamic recovery at high strain rates while it increases the rate of dynamic recovery at low strain rates due to its effect on the self-diffusion rate and dislocation climb processes (Dieter, 1987) as shown in Fig. 6. For this reason, it should be expected that the strain rate sensitivity of the high carbon steel would be higher. The experimental data shows the similar effect, for example the strain rate sensitivities for the high carbon and low carbon steels at 1000 °C are 0.18 and 0.12, respectively as presented in Fig. 7. The kinetics of dynamic recrystallization and recovery are affected by the initial austenite grain size as shown in Eqs. (11) and (12) (XR and XD ). For both the low and the high carbon steels, increasing the initial austenite grain size leads to a
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Fig. 5. The progress of dynamic recrystallization at 1000 °C.
Fig. 7. Variation of flow stress at strain of 0.1 at different strain rates for the high and low carbon steels at 950 °C.
Fig. 6. The progress of dynamic recovery at 1000 °C.
higher overall flow stress and peak flow stress as well slower dynamic recrystallization kinetics (Fig. 8). Hence, the holding time can lead to higher peak strains and flow stress. Fig. 9 displays the effect of initial grain size on the peak strain for both kinds of steel. It is expected that with increasing holding time and resulting austenite grain growth, flow stress decreases but it is observed that the flow stress increases for the longer holding time as displayed in Fig. 10. This phenomenon can be attributed to the austenite grain growth and decreasing grain boundaries areas which are suitable sites for the nucleation of dynamically recrystallized new phase (Dieter, 1987). In this situation the kinetics of dynamic recrystallization is decreased, regarding Eqs. (11) and (12) and the dominant flow softening mechanism will be dynamic recovery which leads to a higher peak flow stress and a higher flow stress. However, the effect of initial grain size is more effective at low strain rates where dynamic recrystallization is the dominant flow softening process while at high strain rates this
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659
Fig. 10. Effect of holding time on the low carbon steel flow curve. Fig. 8. Effect of initial austenite grain size on the kinetics of dynamic recrystallization for the high carbon steel.
parameter has a smaller influence on flow behavior.
5. Conclusion
Fig. 9. Effect of initial austenite grain size on the peak strain.
It was observed that carbon causes an increase in the rate of dynamic recovery and recrystallization and therefore a lower overall flow stress at low z conditions, i.e. high temperatures and/or low strain rates. Moreover, in the case of large Zener– Hollomon parameter for both kinds of steel, dynamic recovery is the only softening mechanism. In this condition, due to the effect of carbon on stacking fault energy, the low carbon steel shows a higher rate of dynamic recovery and therefore a lower flow stress. In addition to prior deformation, the initial austenite grain size can significantly change the kinetics of recrystallization and the flow behavior of both the low and high carbon steels. It is observed that increasing the austenite grain size leads to a higher peak and steady state flow stresses and greater peak strain for the case of dynamic recrystallization in both low and high carbon steels.
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S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
Acknowledgements One of the authors (SS) wants to express his warm thanks to Prof. J.J. Jonas for his valuable guidance during the hot deformation experiments which were performed at McGill University.
References Bergstrom, Y., 1970. A dislocation model for stress–strain behavior of polycrystalline a-Fe with special emphasis the variation of the densities of mobile and immobile dislocations. Mater. Sci. Eng. 5, 193. Colas, R., 1996. A model for the hot deformation of lowcarbon steel. J. Mater. Proc. Tech. 62, 180. Dieter, G.E., 1987. Mechanical Metallurgy. McGraw-Hill, New York. Dixon, T.J., Sellars, C.M., Whiteman, J.A., 1996. The effect of carbon content during hot deformation of austenite. In: 37th MWSP Conf. Proc., ISS, vol. XXXIII, p. 705.
Estrin, Y., Mecking, H., 1984. A unified phenomenological description of work hardening and creep based on oneparameter models. Acta Metall. 32, 57. Honeycombe, R.W.K., 1981. Steels Microstructure and Properties. Edward Arnold, London. Jaipal, J., Davis, C.H.J., Wynne, B.P., Collinson, D.C., Brownrig, A., Hodgson P.D., 1997. Effect of carbon content on the hot flow stress and dynamic recrystallization behaviour of plain carbon steels. In: Proceedings of the International Conference on Thermo-Mechanical Processing of Steels and Other Materials, Wollongong, 7–11 July, p. 539. Kong, L.X., Hodgson, P.D., Collinson, D.C., 1998. Modelling the effect of carbon content on hot strength of steels using a modified artificial neural network. ISIJ Int. 38, 1121. Sellars, C.M., Whiteman, J.A., 1979. Recrystallization and grain growth in hot rolling. Met. Sci. 13, 187. Wray, P.J., 1982. Effect of carbon content on the plastic flow of plain carbon steels at elevated temperatures. Met. Trans. 13A, 125. Wray, P.J., 1984. Effect of composition and initial grain size on the dynamic recrystallization of austenite in plain carbon steels. Met. Trans. 15A, 2009.
An investigation into the effect of carbon on the kinetics of dynamic restoration and flow behavior of carbon steels Siamak Serajzadeh *, Ali Karimi Taheri Department of Materials Science and Engineering, Sharif University of Technology, Azadi Ave., PO Box 11365-9466, Tehran, Iran Received 15 March 2002; received in revised form 21 August 2002
Abstract A study has been made to determine the influence of the carbon content on the kinetics of dynamic recrystallization and recovery as well as flow stress during hot deformation of carbon steels. For this purpose, single hit hot compression experiments at various strain rates and temperatures on two grades of carbon steel together with the Avrami-type kinetics equation and Bergstrom approach have been utilized. The results show that the apparent hot deformation activation energy decreases with increasing carbon content and this phenomenon results in a faster dynamic recrystallization and recovery and a lower flow stress at high temperatures and/or low strain rates in high carbon steels, while at low temperatures and/or high strain rates the low carbon steel has a lower flow stress and higher rate of dynamic recovery. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Phase transformation; Hot compression test; Carbon steel; Flow stress
1. Introduction The flow behavior of steel has always been of importance, because of its strong influence on the microstructure and mechanical properties of the final product. Different factors may alter the flow behavior during the hot deformation of metals. Among these factors the chemical composition has a strong role (Dieter, 1987). Carbon is one of the most important alloy elements which can change the flow behavior as well as the microstructure and kinetics of metallurgical transformation of steel.
*
Corresponding author. Tel.: +98-602-2721; fax: +98-6005717. E-mail address: [email protected] (S. Serajzadeh).
However, there are limited studies dealing with the effect of carbon content on the hot deformation of steels. Wray (1982, 1984) performed hot tension tests at different temperatures to determine the effect of carbon on the flow stress at low strain rates of 6 106 to 2 102 s1 . He reported that increasing the carbon content decreased the work hardening and flow stress of steel. He also suggested an exponentional relationship between the flow stress and temperature. Jaipal et al. (1997) investigated the flow stress and dynamic recrystallization in low and high carbon steel employing a wide range of strain rates. The results of their work show that increasing the carbon content decreased the flow stress of steel at low strain rates and/or high temperatures. Moreover, they reported that at very high strain rates or low temperatures,
0167-6636/03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0167-6636(02)00291-0
654
S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
the peak flow stress of high carbon steel would be higher than that of low carbon steel. Kong et al. (1998) have modeled the effect of carbon content on the hot strength of steel. They demonstrated that increasing the carbon content decreases the flow stress at low strain rates and/or high temperatures whilst at high strain rates and/or low temperatures the low carbon steel has a lower flow stress especially at the initial stage of deformation. The effect of carbon and initial austenite grain size on the austenite flow stress were studied by Dixon et al. (1996). They demonstrated that low carbon steels have a higher strength at strain rates below 1 s1 . Above 1 s1 high carbon steels are stronger and also, there is a little change in recrystallization kinetics between low and high carbon steels. Although the effect of carbon on hot deformation of steel has been studied, because of the complex role of carbon on the flow behavior of steel the study of the effect of carbon on restoration phenomenon in steel requires further investigation. In the present paper, hot compression tests at different strain rates and temperatures were used to study the effect of carbon content and initial austenite grain size on the kinetics of dynamic recrystallization and recovery as well as on the flow behavior of steel in the austenite range. Also, a mathematical model of the flow stress and the kinetics of dynamic recrystallization and recovery via the Bergstrom approach (1970) and the Avrami-type equation will be presented.
2. Transformation and flow stress model
q ¼ q0
ð1Þ
at e ¼ 0
ð2Þ
So, the dislocation density variations during hot deformation can be described as U Xe U Xe e þ q0 q¼e ð3Þ X X Utilizing Eq. (1) and calculating dislocation density for the steady state flow stress condition, we have dq ¼ 0; de
qRec ¼
U X
ð4Þ
Also, using the classic relationship between stress and dislocation density (Honeycombe, 1981), r ¼ aGbq0:5 , and employing Eqs. (3) and (4), it can be found that the variation of flow stress due to dynamic recovery during hot deformation is as follows: r2 ¼ r2Rec þ ðr20 r2Rec ÞeXe ð5Þ where r is the instantaneous flow stress, r0 and rRec are the initial flow stress and the steady state flow stress due to dynamic recovery, respectively. During hot deformation, one may ignore the initial flow stress due to its low magnitude (Colas, 1996). In this condition Eq. (5) can be written as XR ¼
Various models have been proposed to describe the flow stress of metals during hot deformation incorporating dynamic recrystallization and recovery (Bergstrom, 1970; Estrin and Mecking, 1984). Most of these approaches are based on the balance between work hardening and work softening due to dislocation multiplication and annihilation during hot deformation. Bergstrom (1970) has derived the variation of dislocation density according to work hardening and softening as follows: dq ¼ U Xq de
where U represents the work hardening and X describes the amount of the dynamic recovery during hot deformation. Assuming U and X are strain independent, the above differential equation can be easily solved using the following initial condition:
r2 ¼ 1 expðXeÞ ðe < ec Þ r2Rec
ð6Þ
here XR represents the fraction of dynamic recovery. At high temperatures and low strain rates dynamic recrystallization can occur. In this situation the effect of dynamic recrystallization can be assessed using the Avrami equation (Sellars and Whiteman, 1979) as presented below: n e ec d XD ¼ 1 exp k ð7Þ ðe P ec Þ ep where XD is dynamic recrystallization volume fraction, k and nd are dynamic recrystallization parameters depending on chemical composition
S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
and hot deformation conditions (Colas, 1996), ec is the critical strain for occurring dynamic recrystallization which has been taken 0:8ep (Sellars and Whiteman, 1979) and ep is the peak strain which can be expressed by the following relationship: ep ¼
Ad0q zm
ð8Þ
where z is the Zener–Hollomon parameter, z ¼ e_ expðQdef =RT Þ, and d0 is the initial austenite grain size. It is worth noting that for determining the progress of dynamic recrystallization, XD , the following expression was employed: rRec r XD ¼ ð9Þ rp rRex Here, rRex and rp are the steady state flow stress due to dynamic recrystallization and peak flow stress, respectively. rRec was derived through an extrapolation method using MATLAB. With the aid of Eqs. (6), (7) and (9), the flow stress of steel during hot deformation can be described. It is worth noting that parameters such as rRex , r0 , rRec , X and k are a function of deformation process (Dieter, 1987). They may be described using the Zener–Hollomon parameter while Qdef can be determined by the following relationship (Kong et al., 1998): Q oðln e_Þ ¼ 1 ð10Þ R o T rss
3. Materials and experimental procedures The materials used in this research consisted of two grades of carbon steel with the chemical compositions shown in Table 1. To remove the casting structure, the steels were heated up to 1250 °C and rolled at this temperature. Hot compression samples were machined out of the as received hot rolled bars with the deformation axis parallel to hot rolling direction. A height to diameter ratio of 1.5 was selected for the samples to ensure homogeneous deformation. The hot deformation experiments were conducted on a computerized servohydraulic MTS machine with maximum capacity of 100 kN. Experiments were carried out at
655
Table 1 Chemical composition of the high and low carbon steels (wt.%) C
Mn
Si
P (max)
S (max)
Cr (max)
N (ppm)
B (ppm)
0.7 0.1
0.55 0.5
0.08 0.04
0.03 0.025
0.03 0.025
0.08 0.07
120 80
15 5
Table 2 The deformation parameters used for hot compression tests Temperature (°C)
Strain-rate (s1 )
900 950 1000 1050 1100 1150 1200
0.01 0.1 0.5 1 1.5 2 3
temperatures of 900–1200 °C with strain rates varying between 0.01 and 3 s1 . The employed deformation parameters for the single hit hot compression experiments are presented in Table 2. All samples were heated to 1200 °C and held for 10 min at this temperature and then cooled to the deformation temperature and held for 3 min to eliminate the thermal gradient before deformation at the appropriate true strain rate. To determine the effect of initial austenite grain size the above procedures were performed at different holding times of 20 and 30 min at different temperatures. To reveal the initial austenite grain size an etching solution based on saturated picric acid was utilized at 60 and 80 °C for the high and low carbon steel, respectively.
4. Results and discussion Examples of the stress–strain curves gained from the hot compression tests for the low and high carbon steel are presented in Figs. 1 and 2, respectively. As it is seen from the figures the shapes of all curves are similar to the classical stress–strain curves consisting of initial work hardening at lower strains followed by work softening and a peak in flow stress and then the steady
656
S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
state flow stress region at higher strains. Also, it is observed that for both kinds of steels increasing the strain rate leads to a larger peak in strain and stress. It is worth noting that the high carbon steel has a lower overall flow stress in comparison with the low carbon steel. In addition the peak strain occurs at smaller strains in the high carbon steel. However, at higher strain rates the situation is changed and the low carbon steel has a lower overall flow stress. Based on the data obtained from the hot deformation tests and Eqs. (6) and (7) the following equations for describing the kinetics of dynamic recrystallization and recovery kinetics as well as instantaneous flow stress of steels were derived: low carbon steel: r2 ¼ r2Rec ð1 expð520d00:3 z0:08 eÞÞ ðe 6 ec Þ i h XD ¼ 1 exp 17:2 104 d00:48 z0:23 ðeec Þ1:6
ð11Þ
ðe P ec Þ Fig. 1. Stress–strain curves for the low carbon steel at 1000 °C.
ep ¼ 6:5 104 d00:43 z0:132
high carbon steel: r2 ¼ r2Rec ð1 expð230d00:22 z0:06 eÞÞ ðe 6 ec Þ i h XD ¼ 1 exp 85:5 104 d00:46 z0:3 ðe ec Þ1:8
ð12Þ
ðe P ec Þ ep ¼ 2:5 103 d00:4 z0:1
Fig. 2. Stress–strain curves for the high carbon steel at 1000 °C.
The comparison between the derived stress–strain curves by Eqs. (11) and (12) and experimental stress–strain ones for both the low and the high carbon steels are presented in Figs. 3 and 4, respectively. It can be observed that there is a good agreement between the two sets of data that confirms the validity of the model and the assumptions as well as the derived rate equations of the dynamic recovery and recrystallization. Employing Eq. (10), the activation energies for the low carbon and the high carbon steel were calculated, at steady state stresses less than 100 MPa, as 338 and 316 kJ/mole, respectively. In such a condition, it is expected that the higher activation energy causes a higher Zener–Hollomon factor at an equivalent temperature and strain rate, and therefore, for the high carbon steel the onset of dynamic recrystallization occurs at lower strains
S. Serajzadeh, A.K. Taheri / Mechanics of Materials 35 (2003) 653–660
657
Fig. 3. Derived and experimental stress–strain curves for the low carbon steel.
Fig. 4. Derived and experimental stress–strain curves for the high carbon steel.
since the kinetics of dynamic recrystallization is fast as compared to that of the low carbon steel as shown in Fig. 5. This phenomenon decreases the hot strength of the high carbon steel. Furthermore, in addition to the activation energy, the exponent nd can also influence the rate of recrystallization. Regarding Eqs. (11) and (12) (XD ) it is observed that this parameter is 1.8 and 1.6 for the high and low carbon steels, respectively. This follows faster dynamic recrystallization kinetics as presented in Fig. 5. This may be attributed to the effect of carbon on lattice expansion and resulting increase in self-diffusion rate at the high carbon steel (Wray, 1982), which can increase the rate of dynamic recrystallization and recovery in diffusioncontrolled processes. It should be noted that for large Zener–Hollomon parameter (i.e. high strain rates and/or low temperatures) dynamic recrystallization is postponed and the dominant softening mechanism would be only dynamic recovery. Additionally, at high strain rates the recovery
process is controlled by cross slip process (Honeycombe, 1981). It is expected that under this condition, carbon increases the flow stress of steel due to its effect on reduction of stacking fault energy and increase in critical stress for cross slip. Therefore, carbon decreases the rate of dynamic recovery at high strain rates while it increases the rate of dynamic recovery at low strain rates due to its effect on the self-diffusion rate and dislocation climb processes (Dieter, 1987) as shown in Fig. 6. For this reason, it should be expected that the strain rate sensitivity of the high carbon steel would be higher. The experimental data shows the similar effect, for example the strain rate sensitivities for the high carbon and low carbon steels at 1000 °C are 0.18 and 0.12, respectively as presented in Fig. 7. The kinetics of dynamic recrystallization and recovery are affected by the initial austenite grain size as shown in Eqs. (11) and (12) (XR and XD ). For both the low and the high carbon steels, increasing the initial austenite grain size leads to a
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Fig. 5. The progress of dynamic recrystallization at 1000 °C.
Fig. 7. Variation of flow stress at strain of 0.1 at different strain rates for the high and low carbon steels at 950 °C.
Fig. 6. The progress of dynamic recovery at 1000 °C.
higher overall flow stress and peak flow stress as well slower dynamic recrystallization kinetics (Fig. 8). Hence, the holding time can lead to higher peak strains and flow stress. Fig. 9 displays the effect of initial grain size on the peak strain for both kinds of steel. It is expected that with increasing holding time and resulting austenite grain growth, flow stress decreases but it is observed that the flow stress increases for the longer holding time as displayed in Fig. 10. This phenomenon can be attributed to the austenite grain growth and decreasing grain boundaries areas which are suitable sites for the nucleation of dynamically recrystallized new phase (Dieter, 1987). In this situation the kinetics of dynamic recrystallization is decreased, regarding Eqs. (11) and (12) and the dominant flow softening mechanism will be dynamic recovery which leads to a higher peak flow stress and a higher flow stress. However, the effect of initial grain size is more effective at low strain rates where dynamic recrystallization is the dominant flow softening process while at high strain rates this
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Fig. 10. Effect of holding time on the low carbon steel flow curve. Fig. 8. Effect of initial austenite grain size on the kinetics of dynamic recrystallization for the high carbon steel.
parameter has a smaller influence on flow behavior.
5. Conclusion
Fig. 9. Effect of initial austenite grain size on the peak strain.
It was observed that carbon causes an increase in the rate of dynamic recovery and recrystallization and therefore a lower overall flow stress at low z conditions, i.e. high temperatures and/or low strain rates. Moreover, in the case of large Zener– Hollomon parameter for both kinds of steel, dynamic recovery is the only softening mechanism. In this condition, due to the effect of carbon on stacking fault energy, the low carbon steel shows a higher rate of dynamic recovery and therefore a lower flow stress. In addition to prior deformation, the initial austenite grain size can significantly change the kinetics of recrystallization and the flow behavior of both the low and high carbon steels. It is observed that increasing the austenite grain size leads to a higher peak and steady state flow stresses and greater peak strain for the case of dynamic recrystallization in both low and high carbon steels.
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Acknowledgements One of the authors (SS) wants to express his warm thanks to Prof. J.J. Jonas for his valuable guidance during the hot deformation experiments which were performed at McGill University.
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